A spokesman for the club said that the top targets are Joachim Low and Jurgen Klinsmann after the World Cup, however, and there is no rush to appoint their new boss until all options have been investigated.
"The president has given a speech about it," Sky Sports News quotes the spokesman as saying. "He said that we just spoke with David Moyes and he said that he can come to Galatasaray but he is not one of the main targets for us.
"They just spoke to each other, exchanging ideas - that it is it. It is true the president talked with David Moyes. We are not in a rush, we are waiting for the end of the World Cup. The first two targets are Low or Klinsmann."
Galatasaray's previous boss Roberto Mancini left the club earlier in the month.